Model representations of heat shock in terms of dynamic thermal elasticity
https://doi.org/10.32362/2500-316X-2020-8-2-85-108
Abstract
This article is devoted to mathematical models of thermal shock in terms of dynamic thermoelasticity and their application to the specific conditions of intensive heating and cooling of solids. A scheme is proposed for deriving the compatibility equation in voltages for dynamic problems, which generalizes the well-known Beltrami-Mitchell relation for quasistatic cases. The proposed relation can be used to consider numerous special cases in the theory of thermal shock in Cartesian coordinates for both bounded canonical bodies and partially bounded ones. As a detailed study, the latter case was considered under conditions of abrupt temperature heating and cooling, thermal heating and cooling, and medium heating and cooling. Numerical experiments were carried out, and the wave nature of the propagation of thermoelastic waves was described. The effect of relaxation of the solid boundary on sudden heating and sudden cooling, which has been little studied in thermomechanics, is described. It is established that this effect influences maximum of internal temperature stresses, which depend on the parameters characterizing the elastic and thermal properties of materials, as well as the heating time and cooling time. A “compatibility equation” in displacements was proposed to study the problem of thermal shock in cylindrical and spherical coordinate systems in bodies with a radial heat flow and central symmetry. The formulation of a generalized problem in the theory of thermal shock is formulated, which is of practical and theoretical interests for many areas of science and technology.
About the Author
E. M. Kartashov
MIREA – Russian Technological University (M.V. Lomonosov Institute of Fine Chemical Technologies)
Russian Federation
Russian Federation
Eduard M. Kartashov, Dr. Sci. (Physics and Mathematics), Professor of the Department of Higher and Applied Mathematics
86, Vernadskogo pr., Moscow 119571
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1. This article discusses the mathematical models of thermal shock, in terms of dynamic thermoelasticity, and applications to specific conditions of intensive heating and cooling of solids. A scheme is proposed for deriving the compatibility equation (in voltages) for dynamic problems, which generalizes the well-known Beltrami¬–Mitchell equation for quasi-static cases. Numerical experiments have been carried out, and the wave nature of the thermoelastic wave propagation has been described. The effect of relaxation of the solid boundary upon sudden heating and cooling, which has been little studied in thermomechanics, is described. | |
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Kartashov E.M. Model representations of heat shock in terms of dynamic thermal elasticity. Russian Technological Journal. 2020;8(2):85-108. (In Russ.) https://doi.org/10.32362/2500-316X-2020-8-2-85-108
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